Tag Archives: traffic jams

Countless hours are lost in traffic jams every year. Most frustrating of all are those jams with no apparent cause — no accident, no stalled vehicle, no lanes closed for construction.

Such phantom jams can form when there is a heavy volume of cars on the road. In that high density of traffic, small disturbances (a driver hitting the brake too hard, or getting too close to another car) can quickly become amplified into a full-blown, self-sustaining traffic jam.

A team of MIT mathematicians has developed a model that describes how and under what conditions such jams form, which could help road designers minimize the odds of their formation. The researchers reported their findings May 26 in the online edition of Physical Review E.

Key to the new study is the realization that the mathematics of such jams, which the researchers call “jamitons,” are strikingly similar to the equations that describe detonation waves produced by explosions, says Aslan Kasimov, lecturer in MIT’s Department of Mathematics. That discovery enabled the team to solve traffic jam equations that were first theorized in the 1950s.

The equations, similar to those used to describe fluid mechanics, model traffic jams as a self-sustaining wave. Variables such as traffic speed and traffic density are used to calculate the conditions under which a jamiton will form and how fast it will spread.

Once such a jam is formed, it’s almost impossible to break up — drivers just have to wait it out, says Morris Flynn, lead author of the paper. However, the model could help engineers design roads with enough capacity to keep traffic density low enough to minimize the occurrence of such jams, says Flynn, a former MIT math instructor now at the University of Alberta.

The model can also help determine safe speed limits and identify stretches of road where high densities of traffic — hot spots for accidents — are likely to form.

Flynn and Kasimov worked with MIT math instructors Jean-Christophe Nave and Benjamin Seibold and professor of applied mathematics Rodolfo Rosales on this study.

The team tackled the problem last year after a group of Japanese researchers experimentally demonstrated the formation of jamitons on a circular roadway. Drivers were told to travel 30 kilometers per hour and maintain a constant distance from other cars. Very quickly, disturbances appeared and a phantom jam formed. The denser the traffic, the faster the jams formed.

“We wanted to describe this using a mathematical model similar to that of fluid flow,” said Kasimov, whose main research focus is detonation waves. He and his co-authors found that, like detonation waves, jamitons have a “sonic point,” which separates the traffic flow into upstream and downstream components. Much like the event horizon of a black hole, the sonic point precludes communication between these distinct components so that, for example, information about free-flowing conditions just beyond the front of the jam can’t reach drivers behind the sonic point. As a result, drivers stuck in dense traffic may have no idea that the jam has no external cause, such as an accident or other bottleneck. Correspondingly, they don’t appreciate that traffic conditions are soon to improve and drive accordingly.

“You’re stuck in traffic until all of the sudden it just clears,” says Morris.

In future studies, the team plans to look more detailed aspects of jamiton formation, including how the number of lanes affects the phantom traffic jams.

The research was funded by the U.S. Air Force Office of Scientific Research, the National Science Foundation and the (Canadian) Natural Science and Engineering Research Council.

(12-03) 19:54 PST — The problem with the proposal to charge a toll to drive in crowded areas of San Francisco during rush hour is that the logic behind the idea is backward.

The standard line is that those stubborn, heedless drivers are refusing to get out of their cars. Therefore, we need to force them by bonking them with a “congestive pricing” toll of $3 when they enter or leave designated areas of the city. It is tough love, but proponents say people in the Bay Area just won’t use public transit unless you make them.

Really? Tell that to the commuters in the East Bay who would love to ride BART but can’t find parking at the stations. Or the Caltrain passengers who find train cars packed to the gills. Or Richmond District resident Susan Fry, a marketing copywriter who works downtown. Considering the walk to her bus stop, a 40-minute ride during commute hours, and a hike to her office, Fry said taking Muni is no bargain.

“I am probably one of the few people who likes to take the bus,” she said. “My complaint is that I am only 6 miles from where I want to go and it takes me 45 minutes to get there.”

Congestive pricing is classic San Francisco problem solving. Given the choice between a bold, sweeping and innovative new idea that will make headlines across the country and a basic, nuts-and-bolts solution that isn’t sexy, we go for the big splash every time. C’mon, it isn’t that people don’t want to use public transit – this is one of the greenest cities in the country. It is that the public transit we have isn’t a good alternative.

Members of San Francisco County Transportation Authority, who are spearheading the discussion of the issue, admit there are problems.

“We totally get that,” said Tilly Chang, deputy director of planning for the authority. “With Muni, the issue is crowding and reliability, with BART it is getting a seat and a parking place, and Caltrain is really running at capacity. And frankly, the travel times are just not competitive in some cases.”

So why are we trying to push people into transit options that are not working?

“You get all these people out of their cars and where do they go?” asked Tim Leonoudakis, CEO of City Park, a major parking-garage firm. “This is putting the cart before the horse.”

The real issue, you will not be surprised to learn, is money. Chang and others at the authority have referenced London as a good example of the success of the program. As it happened, four students from London’s King’s College were at the Tuesday night workshop. They were studying transit issues in the city, but I asked them about their impressions of London’s toll system that was implemented in 2003.

In general they are supportive of the toll, but they have grave misgivings about bringing it to San Francisco. They raved about London’s comprehensive bus and subway service. That’s why the toll system works there.

“London’s transportation system was already in place,” said Louis Loundy. “This is a time when the U.S. government needs to introduce money into public transit. Then you can introduce this plan.”

In the current economic climate, good luck with that, although the promise of federal dollars has a lot to do with the impetus for this plan.

“The Department of Transportation has expressed a desire for some city to step up and try this,” Chang said. “There are no promises of how much money might be available, but they offered $350 million to New York.”

New York, however, decided not to go ahead with the idea, citing a series of problems. For example, London needed roughly $200 million to get the toll plan off the ground, and everyone admits that administrative costs have been much higher than expected. Today, King’s College student Shaun Bradford said, the program is making money – but that’s after nearly six years of shaking out the kinks.

It makes you wonder about the numbers the proponents keep throwing out. Between $35 million and $60 million will be generated each year, they say. Add that to the funds the advocates hope to get from the federal government, and they insist it will all come together. The money will dramatically improve mass transit, fewer people will want to drive in the city, and more of them will happily get aboard the bus, or BART, or Caltrain.

Let’s see, just throw more money at public transit and everything will improve. Have we heard that before? You bet we have and the problems persist.

As Jason Jungreis, a member of the board of the Planning Association for the Richmond District and opponent of congestive pricing likes to say, “If public transit were a preferable alternative, it would already be preferred.”